Question: Simplify the following expression: $t = \dfrac{-5y^2 + 55y - 150}{y - 5} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ t =\dfrac{-5(y^2 - 11y + 30)}{y - 5} $ Then we factor the remaining polynomial: $y^2 {-11}y + {30} $ ${-5} {-6} = {-11}$ ${-5} \times {-6} = {30}$ $ (y {-5}) (y {-6}) $ This gives us a factored expression: $\dfrac{-5(y {-5}) (y {-6})}{y - 5}$ We can divide the numerator and denominator by $(y + 5)$ on condition that $y \neq 5$ Therefore $t = -5(y - 6); y \neq 5$